cordenadas cartesianas​

Answer:

B. 12cm

Step-by-step explanation:

We can double check by plugging in the number. However, the question trys to trick you, by giving you the diametre, but in order for the formula to work (V=4 /3πr^3), we will divide the diametre by 2 (12 ÷ 2= 6),

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Once we do that, we can double check, when you plug in your numbers your answer will be around 900 (904.78, to be exact, but the question asks for approximate diamtetre).

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Have a good day :)

The present value of $2,500 per year for 10 years discounted back to the present at 7 percent is $17,462.03.

To calculate the present value of an ordinary annuity, we can use the formula:

PV = A * [1 - (1 + r)^(-n)] / r,

where PV is the present value, A is the annual payment, r is the discount rate per period, and n is the number of periods.

In this case, the annual payment is $2,500, the discount rate is 7 percent (or 0.07 as a decimal), and the number of periods is 10 years. Plugging in these values into the formula, we can calculate the present value:

PV = $2,500 * [1 - (1 + 0.07)^(-10)] / 0.07 ≈ $17,462.03.

Therefore, the present value of $2,500 per year for 10 years discounted back to the present at 7 percent is approximately $17,462.03. This represents the amount of money needed in the present to be equivalent to receiving $2,500 per year for 10 years with a 7 percent discount rate.

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The possible approximate lengths of b are: 2.3 units and 7.8 units

We know that the law of sines for triangle is:

The ratios of the length of all sides of a triangle to the sine of the respective opposite angles are in proportion.

This means, for triangle ABC,

\(\frac{sin~ A}{a} =\frac{sin~B}{b} =\frac{sin~ C}{c}\)

where a is the length of side BC,

b is the length of side AC,

c is the length of side AB.

For triangle ABC consider an equation from sine law,

\(\frac{sin~ A}{a} =\frac{sin~ C}{c}\)

here, c = 5.4, a = 3.3, and m∠A = 20°

\(\frac{sin~ 20}{3.3} =\frac{sin~ C}{5.4}\\\\\frac{0.3420}{3.3} =\frac{sin~ C}{5.4}\)

0.3420 × 5.4 = 3.3 × sin(C)

sin(C) = 0.5596

∠C = arcsin(0.5596)

∠C = 34.03°  OR 145.9°

∠C ≈ 34° OR 146°

We know that the sum of all angles of triangle is 180 degrees.

so, ∠A + ∠B + ∠C = 180°

when m∠C = 34°,

20° + ∠B + 34.03° = 180°

∠B = 125.97°

m∠B = 126°

when m∠C = 146°,

20° + ∠B + 146° = 180°

m∠B = 14°

Now consider equation,

\(\frac{sin~ A}{a} =\frac{sin~ B}{b}\\\\\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 126^{\circ}}{b}\)

b × 0.3420 = 0.8090 × 3.3

b = 7.8 units

when m∠B = 14°,

\(\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 14^{\circ}}{b}\)

b × 0.3420 = 0.2419 × 3.3

b = 2.3 units

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The complete question is:

Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction

In ΔABC, c = 5.4, a = 3.3, and measure of angle A = 20 degrees. What are the possible approximate lengths of b? Use the law of sines to find the answer.

2.0 units and 4.6 units

2.1 units and 8.7 units

2.3 units and 7.8 units

2.6 units and 6.6 units

The height of the monument is 201 ft

The angle of elevation is 63.6

Sine of B is equal to

The height of the monument is solved using trigonometry, The angle of elevation is first calculated using cosine

cos (angle of elevation) = 100 / 225

angle of elevation = arc cos (100 / 225)

angle of elevation =  63.612 degrees

The height, h

tan 63.6 = h / 100

h = 100 * tan 63.6

h = 201.449

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Answer

9th graders in her school

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A is wrong because the teachers are not in 9th grade.

B is wrong because parents are not in 9th grade

D is wrong because the homeroom does not represent the entirety of 9th grade

The problem that Bradley could he be trying to solve is C. A person can afford a $350-per-month loan payment. If she is

being offered a 3-year loan with an APR of 0.8%, compounded monthly, what is the most money that she can borrow?

From the information, Bradley entered the following group of values into the TVM Solver of his graphing calculator. N = 36; 1% = 0.8; PV =; PMT = -350; FV = 0; P/Y = 12; C/Y = 12; PMT:END.

Based on this, a person can afford a $350-per-month loan payment. If she is being offered a 3-year loan with an APR of 0.8%.

The correct option is C

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Bradley entered the following group of values into the TVM Solver of his

graphing calculator. N = 36; 1% = 0.8; PV =; PMT = -350; FV = 0; P/Y = 12; C/Y

= 12; PMT:END. Which of these problems could he be trying to solve?

O

A. A person can afford a $350-per-month loan payment. If she is

being offered a 36-year loan with an APR of 9.6%, compounded

monthly, what is the most money that she can borrow?

O

B. A person can afford a $350-per-month loan payment. If she is

being offered a 3-year loan with an APR of 9.6%, compounded

monthly, what is the most money that she can borrow?

O

C. A person can afford a $350-per-month loan payment. If she is

being offered a 3-year loan with an APR of 0.8%, compounded

monthly, what is the most money that she can borrow?

D. A person can afford a $350-per-month loan payment. If she is

being offered a 36-year loan with an APR of 0.8%, compounded

The first term, a1, in the geometric series is -3.

What is Geometric Series?

A geometric series is a series for which the ratio of two consecutive terms is a constant function of the summation index. The more general case of a ratio and a rational sum-index function produces a series called a hypergeometric series. For the simplest case of a ratio equal to a constant, the terms have the form

To find the first term, a1, in a geometric series given the sum, Sn = 93, the common ratio, r = 2, and the number of terms, n = 5, we can use the formula for the sum of a geometric series:

Sn = a1 * (1 - r^n) / (1 - r)

Plugging in the given values, we have:

93 = a1 * (1 - 2^5) / (1 - 2)

Simplifying the expression:

93 = a1 * (1 - 32) / (-1)

93 = a1 * (-31)

Now we can solve for a1 by dividing both sides of the equation by -31:

a1 = 93 / -31

a1 = -3

Therefore, the first term, a1, in the geometric series is -3.

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Answer:

(7, 24)

Step-by-step explanation:

Solve the system:

6x - 18 = 8x - 32

2x = 14

x = 7

y = 6(7) - 18

y = 24

Given data:

The given deck of card.

The probability of even number card or face card is,

Thus, the probability of even number card or face card is 4/13.

The probability of numbered card or heart is,

Thus, the probability of numbered card or heart is 10/13.

The area bounded by the curves x = 25 - √(y - 5) and x = y - 10, bounded below by the x-axis, is approximately 324.24 square units.

To calculate the area bounded by the curves x = 25 - √(y - 5) and x = y - 10, bounded below by the x-axis, we need to find the intersection points of the curves and integrate the area between those points.

First, let's find the intersection points by setting the two equations equal to each other:

25 - √(y - 5) = y - 10

To solve this equation, we can square both sides:

(25 - √(y - 5))^2 = (y - 10)^2

Expanding and simplifying, we get:

625 - 50√(y - 5) + y - 5 = y^2 - 20y + 100

Rearranging terms, we have:

y^2 - 20y + 100 - y + 50√(y - 5) - 625 + 5 = 0

Simplifying further:

y^2 - 21y - 520 + 50√(y - 5) = 0

We can solve this equation numerically to find the intersection points using methods such as the Newton-Raphson method or graphing calculators.

Approximate solutions are y ≈ 26.63 and y ≈ -0.378.

To integrate the area, we need to find the limits of integration. Since we are bounded below by the x-axis, the lower limit will be the x-coordinate where the curves intersect the x-axis.

For the curve x = 25 - √(y - 5), we can set x = 0:

0 = 25 - √(y - 5)

Solving for y, we get:

√(y - 5) = 25

y - 5 = 625

y ≈ 630

So

The upper limit of integration will be the y-coordinate where the curves intersect:

y = 26.63

Now, we can integrate the function x = y - 10 from y = 630 to y = 26.63 to find the area:

Area = ∫[630, 26.63] (y - 10) dy

Integrating the function, we get:

Area = [0.5y^2 - 10y] evaluated from 630 to 26.63

Area = (0.5(26.63)^2 - 10(26.63)) - (0.5(630)^2 - 10(630))

Area ≈ 324.24 square units

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B = 2k

A = k√3

C = k

\( \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \)

Length of outer boundary =30m

So area of outer boundary =30×30

= 900m²

Length of inner boundary of path=30-1= 29m

Inner area =29×29 =841m²

So area of path is= outer area - inner area

=900- 841

= 59m²

The fourth and fifth term of this sequence is -30 and -10 respectively.

Data;

The common difference in a geometric progression is the ratio between two successive terms.

Let's find the common difference in this sequence

\(r = \frac{-270}{-810} \\r = \frac{1}{3}\)

The nth term of a geometric sequence is given as

\(T_n = ar^n^-^1\\\)

The next two terms of this sequence will be 4th and 5th term.

The fourth term of this sequence is

\(T_4 = ar^4^-^1\\T_4 = -810 * (\frac{1}{3})^3\\ T_4 = -810 * \frac{1}{27}\\ T_4 = -30\)

The fifth term of this sequence is

\(T_5 = ar^5^-^1\\T_5 = -810 * (\frac{1}{3})^4\\T_5 = -810 * \frac{1}{81} \\T_5 = -10\)

The fourth and fifth term of this sequence is -30 and -10 respectively.

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First you will get 4dz

the slope of that equation is -3/5

Answer:

its C bro

its have to be 1-sin2x

because (sinx-cosx)² equal sin²x+cos²x-2×sinx×cosx

Answer:

1. 220

2. 260

3. 1400

4. 5160

Step-by-step explanation:

1. 11 out of 15

300 ÷ 15 = 20

20 x 11 = 220

2. 13 out of 20

400 ÷ 20 = 20

20 x 13 = 260

3. 2 out of 5

3500 ÷ 5 = 700

700 x 2 = 1400

4. 129 out of 300

12000 ÷ 300 = 40

40 x 129 = 5160

Answer:

14

Step-by-step explanation:

100% is 20

meaning that for every ten percent is two

so if you minus 30% 6 from 100% 20 you get 14

The fraction 9/80 cannot be simplified further, so that is the final answer.

Claudia has a total of 16/3 gallons of paint, and 3/5 gallons of that amount is red. To determine the fraction of Claudia's paint that is red, we need to express the amount of red paint as a fraction of the total amount of paint.

Let's denote the fraction of red paint as r and the total amount of paint as p.

We know that the amount of red paint is 3/5 gallons, which can be expressed as r = 3/5.

The total amount of paint is 16/3 gallons, which can be expressed as p = 16/3.

To find the fraction of Claudia's paint that is red, we divide the amount of red paint by the total amount of paint:

Fraction of red paint = r/p = (3/5) / (16/3).

To divide fractions, we multiply the numerator of the first fraction by the denominator of the second fraction and the denominator of the first fraction by the numerator of the second fraction:

Fraction of red paint = (3/5) * (3/16) = 9/80.

Therefore, the fraction of Claudia's paint that is red is 9/80.

It's important to note that fractions should be simplified if possible. In this case, the fraction 9/80 cannot be simplified further, so that is the final answer.

In conclusion, the fraction of Claudia's paint that is red is 9/80.

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The power rule for logarithms states that logb(M^p) = p * logb(M). The logarithm of a number with an exponent is the product of the exponent and the logarithm of that number.

The power rule states that logb(M^p) = p * logb(M), where M, b, and p are positive real numbers.

To understand this rule, let's consider an example. Suppose we have log2(8^2). According to the power rule, this is equivalent to 2 * log2(8).

In this case, M is 8, b is 2, and p is 2. The power rule tells us that we can bring the exponent (p) down and multiply it with the logarithm of the base (b) raised to the number (M).

So, log2(8^2) can be simplified as 2 * log2(8), which is 2 * 3 = 6.

In general, the power rule allows us to simplify logarithmic expressions by bringing the exponent down and multiplying it with the logarithm of the base.

This rule is particularly useful when dealing with complex logarithmic expressions and simplifying them to a more manageable form.

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Based on the given information, Carl's car wash takes a constant time of 4.5 minutes in its automated car wash cycle. Autos arrive following a Poisson distribution at the rate of 10 per hour. Using this information, Carl can calculate the expected time it would take to wash a car.

The first step is to calculate the average time between car arrivals, which is equal to 60 minutes divided by the arrival rate of 10 cars per hour, giving an average time of 6 minutes per car. Since the wash cycle time is constant at 4.5 minutes, Carl can add these two values together to get an expected wash time of 10.5 minutes per car.

However, it's important to note that this is just an expected time, and there may be variations due to factors such as queue length, equipment malfunctions, or other unforeseen circumstances. Therefore, Carl should regularly monitor his car wash operation and make adjustments as necessary to ensure efficient and consistent service.

In summary, Carl's car wash takes a constant time of 4.5 minutes in its automated car wash cycle, and with autos arriving at a rate of 10 per hour, the expected time it would take to wash a car is 10.5 minutes.

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a. The common ratio is 2.

Given that the sum of the first five terms of the geometric series is 33, we use the formula for the sum of terms of a geometric series, S

Sₙ = a(rⁿ - 1)/(r - 1) where a = first term and r = common ratio

Since n = 5, the first 5 terms, and S₅ = 33

Sₙ = a(rⁿ - 1)/(r - 1)

33 = a(r⁵ - 1)/(r - 1) (1)

Also, when n = 10, the sum of the first 10 terms is S₁₀ = -1023

So, -1023 = a(r¹⁰ - 1)/(r - 1) (2)

Dividing (2) by (1), we have

-1023/33 = a(r¹⁰ - 1)/(r - 1) ÷ a(r⁵ - 1)/(r - 1)

-31 = (r¹⁰ - 1)/(r⁵ - 1)

-31(r⁵ - 1) = r¹⁰ - 1

-31r⁵ + 31 = r¹⁰ - 1

r¹⁰ - 1 + 31r⁵ - 31 = 0

r¹⁰ + 31r⁵ - 32 = 0

Let r⁵ = y

(r⁵)² + 31r⁵ - 32 = 0

y² + 31y - 32 = 0

Factorizing, we have

y² + 32y - y - 32 = 0

y(y + 32) - (y + 32) = 0

(y - 1)(y - 32) = 0

y - 1 = 0 or y - 32 = 0

y = 1 or y = 32

r⁵ = 1 or r⁵ = 32

r = ⁵√1 or r = ⁵√32

r = 1 or r = 2

Since for a geometric series, r ≠ 1, r = 2.

So, the common ratio is 2.

ii. The first term of the series.

The first term of the series is 33/31

Using (1)

33 = a(r⁵ - 1)/(r - 1) (1) where r = 2,

33 = a(2⁵ - 1)/(2 - 1) (1)

33 = a(32 - 1)/1

33 = 31a

a = 33/31

So, the first term of the series is 33/31

b. Find the general term of the series. Simplify your answer. ​

The general term of the geometric series is (33/62) × 2ⁿ

The general term of a geometric series is Uₙ = arⁿ⁻¹

With a = 33/31 and r = 2,

Uₙ = arⁿ⁻¹

Uₙ = (33/31) × 2ⁿ⁻¹

Uₙ = (33/31) × 2ⁿ/2

Uₙ = (33/62) × 2ⁿ

So, the general term of the geometric series is (33/62) × 2ⁿ

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Answer:

1/4, 4/10, 3/7, 24/50 are all less than 1/2.

Step-by-step explanation:

For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

The "Rule of 72" is a quick estimation method to determine the time it takes for an investment or savings to double in value. By dividing 72 by the interest rate, you can obtain an approximation of the doubling time. For an interest rate of 3%, it would take approximately 24 years for the savings to double. For an interest rate of 8%, it would take around 9 years for the savings to double.

To calculate the doubling time using the Rule of 72, divide 72 by the interest rate. This provides an approximation of the number of years it takes for an investment or savings to double in value.

For an interest rate of 3%, we divide 72 by 3: 72 / 3 = 24. Therefore, it would take approximately 24 years for the savings to double.

For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

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6 + 2 2 = 2 ( 3 + 11 )

60 + 25 = 5 ( 12 + 5 )

For Felipe and Helena's final grades, the solution is option C, [74 71].

Using the given values for Q, T, and P weights and Felipe and Helena's grades, calculate their final grades as follows:

Felipe's final grade:

0.40 x 80 + 0.50 x 60 + 0.10 x 90 = 32 + 30 + 9 = 71

Helena's final grade:

0.40 x 70 + 0.50 x 80 + 0.10 x 60 = 28 + 40 + 6 = 74

To represent the final grades for Felipe and Helena in a matrix F, given formula F = WG, where W = matrix of weights and G = matrix of grades:

[0.40 0.50 0.10]   [80 70]

F = WG = [0.40 0.50 0.10] x [60 80]

[0.40 0.50 0.10] [90 60]

Performing matrix multiplication:

[32 + 30 + 9  28 + 40 + 6]

F = WG = [32 + 40 + 6 28 + 40 + 3]

[36 + 25 + 6 36 + 20 + 3]

Simplifying:

[71 74]

F = WG = [78 71]

[67 59]

Therefore, [74 71] for Felipe and Helena's final grades, respectively.

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The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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The length of the model car based on the information is 0.8 feet.

It should be noted that scale simply shows the relationship between a measurement on a model as well as the corresponding measurement on the actual object.

From the information, the model car is constructed with a scale of 1:15.

When the actual car is 12 feet long, the length of the model will be illustrated as x. This will be:

= 1/15 = x / 12

Cross multiply

15x = 1 × 12

15x = 12

Divide

x = 12 / 15

x = 0.8

The length is 0.8 feet.

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Answer:

102cm²

Step-by-step explanation:

Step 1 find the area of the whole rectangle

Area of a rectangle = width times length

The width of the rectangle is 20 cm and the length is 6cm

So the area = 20 * 6

20 * 6 = 120

Hence the area of the rectangle is 120 square centimeters.

Step 2 Find the area of the square and the triangle

Area of square = s²

where s = side length

The square has a side length of 3 so the area of the square = 3²

3² = 9

Hence, the area of the square is 9cm²

Now to find the area of the triangle

area of a triangle = \(\frac{bh}{2}\) where b = base length and h = height

We are given the height (3 cm, this is given because the square is sharing it's side length with the height of the triangle.)

Now to find the base length

We can find it by subtracting the overall rectangle's width (20cm) by the bottom width (11 cm) and the bottom length of the square ( 3 cm )

so triangle's base length = 20 - 11 - 3

20 - 11 - 3 = 6

so the base length of the triangle is 6 cm

now we plug in the values of the height and the base length into the formula

\(A=\frac{6*3}{2} \\6*3=18\\\frac{18}{2} =9\)

Hence the area of the triangle is 9 cm²

Finally, to find the area of the shaded area, we subtract the area of the triangle and the area of the square from the area of the rectangle

so your answer = 120 - 9 - 9

120 - 9 - 9 = 102

Hence, the area of the shaded region is 102 square centimeters.